Shinies in Let's Go are actually kind of hard to keep up with.
I finally got my shiny Vulpix, maxed its AVs with Vulpix Candy, beat the Vulpix master, evolved to shiny Ninetales, and beat the Ninetales master.
finally ended my Vulpix combo by catching a shiny Chansey
I'm now on a combo for Bulbasuar. before I even got to 10, I found a shiny Weedle and caught it since the combo was so low
then I worked on getting my Bulbasuar combo really going. I have since caught one shiny Bulbasaur of my desired 3, and run away from the following shinies:
Weedle #2
Pidgey
Weedle #3
Pidgey #2
Weedle #4
Kakuna
Bellsprout
Shiny Bulbasaur #2 is Modest with perfect Special Attack, Special Defense, Attack, and Defense. Continuing for the third and moving on to Charmander. Since I already have a good special attacker, I'm planning on going for Adamant or Jolly to make a Mega X-focused Charizard.